Perceptions of Randomness and Habit Formation among Lottery Gamblers

1
Perceptions of Randomness and Habit Formation
among Lottery Gamblers
2
Motivation

• Large literature in both economics and psychology
  documenting mistaken perceptions of randomness...
• Gamblers fallacy - belief in negative
  auto-correlation
• Laboratory evidence people can not recognize or
  generate random sequences (Wagenaar 1972, Bar
  Hillel Wagenaar 1991)
• Some evidence that in picking numbers, lottery
  gamblers exhibit gamblers fallacy (Clotfelter
  Cook 1993, Terrell 1994)
• Hot hand myth belief in streaks
• e.g. in basketball (Gilovich, Vallone, Tversky
  1985)
• Finance literature mutual fund flows chase high
  returns (Carhart 1997, Chevalier Ellison
  1997,1999, Grinblatt Keloharju 2001, Odean
  1998)
• Law of small numbers Tversky Kahneman (1971)
  small samples resemble population overly
  closely
• We ask whether lottery gamblers appear to believe
  that lightning will strike twice when it comes
  to the sale of a winning ticket.

3
Do consumers respond to the sale of a winner?

• Due to random assignment of winner (conditional
  on ticket sales), any subsequent increase in
  sales can be interpreted as causally related to
  the sale of a winner.
• Advantages of lottery context
• True randomness Financial signals (or basketball
  shots) may have real information, but the sale of
  a winning ticket does not affect the likelihood
  that the retailer will sell a winning ticket in
  the future. (So, if fully informed consumers
  treat lottery tickets as financial assets, should
  be no response.)
• Observed decisions reflect consumption choices
  with real costs for consumers.
• A broad population of individuals engages in
  lottery gambling 40B a year industry about
  half of American adults report playing annually.
• State lotteries are government-operated
  monopolies - whether lottery gamblers are
  rational informed potentially has policy
  implications

4
Overview of findings

• Regarding the initial response to the sale of a
  winner
• Same-store same-game sales increase by 12-38.
• Two interpretations lucky store,
  information/advertising
• The sales response increases in the size of
  jackpot.
• The sales response increases in the proportion of
  the population comprised of economically-disadvant
  aged groups.
• We test for substitution across games and across
  stores - the initial increase in same-store,
  same-game sales reflects a net increase in total
  zip-code level sales.

5
Is lottery gambling habit forming/addictive?

• Since the sale of a winning ticket constitutes an
  exogenous shock to lottery gambling consumption,
  it can be used to test whether any resulting
  increase in lottery consumption is persistent.
• Persistence as habit formation/addiction
• Economics literature defines a good as addictive
  if past consumption causally increases current
  consumption by increasing MU of consumption (e.g.
  Pollack 1970, Becker and Murphy 1988)
• We show that the sale of a winner leads to an
  increase in aggregate sales due to random
  assignment of winner, it is a valid instrument
  for lagged consumption and can thus be used to
  directly test for addiction.
• Note we make no distinction between addiction
  habit formation (consumers develop normal
  levels of consumption that determine MU of
  current consumption) nor do we distinguish b/t
  rational myopic addiction.

6
Overview of findings

• Regarding persistence
• Winning stores experience increases in sales of
  the winning game for up to 40 weeks, but less
  definitive evidence of persistence in increase to
  total zip-code level sales.
• Evidence that buying at the lucky store is
  persistent but mixed evidence regarding whether
  buying lottery tickets in general is addictive
• A small LR increase in aggregate zip code sales,
  but
• Data consistent with LR increase in sales at
  winning vendor and no change in sales at other
  stores.
• Data also consistent with LR increase in sales at
  the winning vendor being driven by a permanent
  substitution away from other vendors.

7
Outline of talk

• Empirical Methodology Data
• Results - initial response
• Interpretation
• Results - persistence
• Interpretation
• Conclusion

8
Empirical methodology

• Separate lags
• git at-1 g-1wi(t-1) f-1gi(t-1) mt eit
• git at-40 g-40wi(t-40) f-40gi(t-40) mt
  eit
• Identifying assumption (in words) Probability of
  selling a winner is a function only of number of
  tickets sold Thus, conditional on lagged sales,
  winner is randomly assigned g has a causal
  interpretation.
• Test of identifying assumption
• git atk gkwi(tk) fkgi(tk) ei(tk)
• Note Serial correlation in sales is not a
  problem for estimation of g, even if f does not
  have a causal interpretation.

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Serial correlation is not a problem for
estimation of g

• P (w1) increases in number of tickets sold so
  due to serial correlation in sales,
• Eeitwit-k1 ? Eeitwit-k0
• But, P(wt-11)P(win)gt-1, where gticket sales
  P(win) is constant, so gt-1 is a sufficient
  statistic for P(wt-11).
• Hence,
• Eeitwit-k1, git-kEeitwit-k0, git-k
• This is identifying assumption that permits a
  casual interpretation

10
Alternative specification

• ai retailer fixed effect
• mt week fixed effect (size of jackpot)
• weakness This has intuitive appeal, but is not
  the empirical representation of the conditional
  randomness it does not control for intertemporal
  variation in sales w/in a retailer.

11
Data Texas lottery sales

• Sample of winners includes lotto games only
• Weekly sales (by game) from Jan 2000 to June 2002
• All 24,400 retailers active at any point during
  this period
• Retailers spread across 3,660 9-digit zip codes
  and 1,386 cities avg of 7 retailers per zipcode,
  18 per city
• TX lottery ticket sales 2.8B/yr
• Avg retailer 2,600/week (games)
• We link sales data to winners information

12
Data Texas lottery winners
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Initial effects same-store, same-game

• Dependent variable ln(weekly retailer sales on
  game j)
• Coefficient on jackpot winner on this game at
  this retailer, t-1

14
Including additional lags doesnt change
qualitative result

15
Initial effects zip-code demographics

• git at-1 g1-1wi(t-1) g2-1(wi(t-1)Xz)
  f-1gi(t-1) b Xz mt eit

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Test of identifying assumption
17
Test of identifying assumption
18
Test of identifying assumption
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Interpretation

• Information effect
• The sale of a jackpot winner serves as
  advertising for the lottery (rational)
• People update subjective probability of winning
  (behavioral?)
• Why store/game-specific? Because flow of
  info/advertising is highly localized.
• Lucky store effect people overinfer from the
  rare event that the store is lucky could be new
  customers or existing customers increasing their
  purchases.

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Advertising practices (Survey)

• Note contract requires use of TLC advertising
  materials
• 5-minute telephone survey of all retail outlets
  that sold winning Lotto TX ticket during the time
  period we observe
• Attempted to contact all 66 stores that sold the
  67 winners
• Asked for manager if not, offered to call back
  if manager new, asked to speak to employee who
  was there for winner
• Of 66 8 had faulty info 14 refused 14 unable
  b/c no current employees there for winner 13
  requested mailed surveys 17 completed

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Advertising practices (Survey)

• Of the 17 winning stores that completed the
  survey -
• 14 report having received some type of media
  attention for having sold a winning lottery
  ticket local newspapers and television stations
  most common.
• 14 report hanging the Winning Ticket Sold Here
  sign provided by the TLC all 14 reporting that
  they displayed the sign immediately following the
  sale of the ticket or as soon as the sign
  arrived.
• 17 report displaying the point of sale materials
  provided by the TLC, such as game decals, game
  posters and display tickets prior to the sale of
  the winning ticket.
• 0 report changing their general advertising
  strategies after the sale of a winning ticket
• 15 report a perceived increase in lottery ticket
  sales following the winning ticket sale
• 9 report a perceived increase in sales of other
  products following the winning ticket sale

22
Some individual-level data Boston/Cambridge
survey

• If the location where you usually buy lottery
  tickets were to sell a winning Massachusetts
  Millions jackpot ticket this week, would it
  affect where you would decide to purchase tickets
  the next time you wanted to play?
• (N78)
• Go to same location 42.3
• Go to same location and buy more tickets 20.5
• Buy tickets from a different location 11.5
• Buy tickets without thinking about where
• a winner was sold 24.4
• Stop buying lottery tickets 1.3

23
Some individual-level data Boston/Cambridge
survey

• If a nearby location other than where you usually
  buy lottery tickets were to sell a winning
  Massachusetts Millions jackpot ticket this week,
  the next time you bought lottery tickets you
  would buy lottery tickets...
• (N81)
• at the location where you most recently bought
  tickets 55.6
• where you most recently bought tickets and
• where the winning ticket was sold 2.5
• at the location that sold a winner instead of
  where you most recently bought tickets 14.8
• w/o thinking about where a winner was sold
  24.7
• at any location except the one that recently
  sold a winner 1.2
• stop buying tickets 1.2

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Net increase? Spillover on other games? Effect
on retailers nonwinning game sales

• Coefficient on a jackpot winner at this retailer
  on game j
• Dep var ln(weekly total retailer sales minus
  sales on game j)

25
Net Increase?Effect on same-game sales in
zipcode

• Coefficient on jackpot winner on game j in
  zipcode dummy
• Dependent variable ln(weekly zipcode sales on
  game j)

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Spillover effect on other stores?Effect on
own-store sales (zip code)

• git at-1 g1-1wi(t-1) g2-1wz(t-1)
  f1-1gi(t-1) f2-1gz(t-1) mt eit
• Interpretation
• g10 increase in same-store sales
• g20 net increase in own-store sales due to
  winner in zip code
• g2winner in zip code
• Note This is run at store-level, so even if
  g2aggregate zip code sales wed have to sum
  reduction (in levels) over all stores in zip code
  and compare to increase (in levels) at winning
  store.

27
Spillover effect on other stores? Effect on
own-store sales (zip code)
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Spillover effect on other stores?Effect on
own-store sales (1-mile)
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In Summary

• There is an increase in same-game sales at the
  winning retailer, and this appears to represent
  an aggregate increase in zip-code sales.
• Because we have a shock to demand, we can
  investigate whether past consumption affects
  future consumption and ask whether lottery
  gambling appears to be addictive

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Addiction/Habit Formation

• Economic literature on addiction
• Intertemporal complementarities (Hicks 1967,
  Pollack 1970) current utility might be a fn of
  not only current C, but past C
• More recent literature on Rational Addiction
  (Stigler and Becker 1977, Becker and Murphy
  1988), incl. empirical tests (Becker, Grossman
  and Murphy 1994, Gruber and Koszegi 2001)
• We only test for existence of addiction
  (economic def) does past consumption of lottery
  tickets lead to future consumption of lottery
  tickets
• We do not distinguish between addiction and habit
  formation
• We do not distinguish between rational and myopic
  addiction (shock is random)
• To interpret persistence as addiction, initial
  effect must have worn off!
• (i.e., pd)

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Persistence same-game, same-store
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Persistence same-game, same-store
33
Persistence same-game, same-store
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Persistence same-game, zipcode
35
Persistence same-game, zipcode
36
Persistence same-game, zipcode
37
Persistence same-game, zipcode
38
Estimating rate of persistence

• Separate lags
• git at-1 g-1wi(t-1) f-1gi(t-1) mt
  ei(t-1)
• git at-40 g-40wi(t-40) f-40gi(t-40) mt
  ei(t-40)
• Consider parametric rate of persistence q
• g-k qk-1 g-1
• Use GMM to solve for q and g-1
• (OLS-estimated coefficients g-1, g-40) are the
  sample moments.)

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Estimated rates of persistence

• Retail-game results for q
• Lotto Texas .959
• Texas Two-Step .994
• Cash 5 .989
• Lotto Texas g-1GMM.285
• g-10 (.959)10.285.188
• g-40 (.959)40.285.053

• Zip-code-game results for q
• Lotto Texas .885
• Texas Two-Step .981
• Cash 5 .903
• Lotto Texas g-1GMM.483
• g-10 (.885)10.483.143
• g-40 (.885)40.483.004

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Possible Interpretations

• Is increase in zip code sales due to
• LR increase in game-specific sales at winning
  store and at other stores in zip code?
• - This would provide evidence of general habit
  formation
• LR increase only at winning store?
• - This could be due to relocated sales (no new
  sales)
• - This could be due to maintained increase at
  winning store, either due to habit
  formation/addiction (new sales persist) or
  persistent belief in lucky store

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The LR Effect of a Winning Ticket within Zip
Code on Retailer Game Sales
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The LR Effect of a Winning Ticket within One
Mile on Retailer Game Sales
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Interpretation Addiction? Habit formation?

• LR increase in game-specific sales at winning
  store.
• New sales (perhaps due to information effect) are
  not clearly sustained, but the increase in the
  wining retailers sales (perhaps) due to a
  shifting is sustained.
• Long-Run Explanations
• Localized advertising continues, general
  advertising has faded (but consider nature of
  local advertising centered on sale of winner)
• Continued belief in the winning vendors luck
  after 10 months
• Consumers who initially thought the store was
  lucky have formed a new habit
• Consumers who increase spending at the winning
  store form new gambling habit.
• Different implications for costs
• Persistent increase in lottery spending is
  costly.
• Persistent shift of purchase location less so.

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Conclusions

• Consumers respond to the sale of a winning
  jackpot ticket could either be a rational
  response to advertising or an irrational belief
  in a lucky store.
• Advertising practices of stores, as well as
  effect of jackpot size, suggest it is not general
  advertising.
• Long-term response suggests habit-formation with
  regard to where to buy tickets or persistent
  belief in lucky store - but data do not provide
  conclusive evidence that lottery gambling in
  general is addictive.
• Long-term response suggests that at least some of
  the initial increase is due to overinference
  about variation in luck across vendors.

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Directions for future work

• Work on adding structure to empirical
  specification in an attempt to increase the power
  of our test for persistence.
• Determine whether new sales are from new
  consumers link data to data on non-lottery
  purchases, e.g. milk. (Potentially scanner data?)
• Individual data. A possibility - Swedish data
  that tracks individual purchases. Or a big
  survey.
• Estimate effect of lottery demand shock on sales
  and prices of other goods.